Question

When a centimeter thick surface is illuminated with light of wavelength $\lambda$, the stopping potential is $\text{V}$. When the same surface is illuminated by light of wavelength $2\lambda$, the stopping potential is $\frac{V}{3}$. Threshold wavelength for the metallic surface is

• A. $\frac{4\lambda }{3}$
• B. $4\lambda$
• C. $6\lambda$
• D. $\frac{8\lambda }{3}$

Answer 1

The correct option is B $4\lambda$

The Einstein's equation of photoelectric effect is given by, $e{V}_0=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$ where e = charge of electron, h = Planck's constant,
$V_0$ = stopping potential, c = velocity of light, $\lambda$ = wavelength of incident light and ${\lambda }_0$ = threshold wavelength
When $V_0=V$
$\Rightarrow eV=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}......\left(i\right)$
and when $V_0=\frac{V}{3}$
$\Rightarrow \frac{eV}{3}=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}.......\left(ii\right)$
from equation (i) and (ii)
$\frac{hc}{3\lambda }-\frac{hc}{3{\lambda }_0}=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}$
or $\frac{2}{3{\lambda }_0}=\frac{1}{6\lambda }$ or ${\lambda }_0=4\lambda$